Love waves of SH type in an inhomogeneous transversely-isotropic elastic medium

The asymptotics of high-frequency Love waves, which are counterparts of transverse surface waves of SH type in isotropic media, is studied for a special type of anisotropy of elastic media. The wave field is represented as the sum of a space-time (ST) caustic expansion and two ST ray series for two faster waves attenuating exponentially with depth. The complex eikonals of these waves and the coefficients of caustic ST and ray series are found by recursion in the form of two-variable expansions: one in the distance from the surface and the other in a small parameter, which characterizes the proximity of the caustic of the ray field to the surface of the elastic body. The specific structure of the elasticity tensor for a transversely-isotropic medium suggests the use of a rectangular coordinate system, hence the surface is to be regarded as a plane. For the elements of the elasticity tensor we obtained relations which accord with the initial formulation of the problem and ensure the initiation of the waves under study. In the formulas deduced, one can easily see the transition from an anisotropic medium to an isotropic one.